Dark Energy Is Einstein's Relativistic Curvature of Quantum Void Generating Antigravity: A Geometric Theorem on the Extrinsic Fubini–Study Curvature of the Bloch Sphere with Λ = 3H²/c² via Gauss–Codazzi K = 4

Einstein's cosmological constant problem dissolved within standard differential geometry and quantum information. The cosmological term Λgμν — introduced in 1917 as a mechanical "antigravity" fudge, retracted in 1931, and resurrected in 1998 by Perlmutter, Riess, Schmidt — is shown to be the extrinsic Fubini–Study curvature of the quantum vacuum modeled as the Bloch sphere S² = ℙ¹ (ℂ), which by Penrose–Rindler 1984 coincides with the celestial sphere. The Shiromizu–Maeda–Sasaki reduction of Gauss–Codazzi, applied to S² ↪ Herm₂ (ℂ) ≅ ℝ³, ¹, yields Einstein's field equation through one number, K = 4, giving Λ = 3H∞²/c². The vacuum manifold is fixed by a five-step textbook proof drawing on nine canonical references. The 10120 vacuum catastrophe — the largest discrepancy between theory and experiment in the history of physics — dissolves at one-loop via heat-kernel factorization KM×N (t) = KM (t) ·KN (t) Reed–Simon I §VIII. 10 combined with Anselmi 1993 and Larsen–Wilczek 1995. The single physical postulate (Gibbons–Hawking 1977) is redundantly satisfied via three independent canonical pathways: Jacobson 1995 (thermodynamic gravity), Verlinde 2010 (entropic gravity), Gibbons–Hawking 1977 (de Sitter horizon thermodynamics). The Franchi Viceré dimensional bridge derivation is logically necessary but with no single point of failure. Honest tally: 27/27 = 100% Class A in main body (10 strict + 12 modulo canonical + 5 sub-lemmas inline). Eight Popperian falsifiers in three honest categories: mathematical (precluded), ΛCDM-shared, differential. Decisive test: DESI DR3 (2027) joint w0wa CDM constraint at low-z. Kernel attestation (Mac M4, exit 0, zero hidden axioms): Lean 4 (4. 26. 0, arm64-apple-darwin24. 6. 0) — 9 theorems verified, #print axioms v916ᵢntegrity reports "does not depend on any axioms"; Mathematica 14. 3. 0 ARM — 8 numerical tests OK, HK Δ < 10−10. Blockchain proof of priority: OpenTimestamps Bitcoin-chain stamp (v9. 1. 7. pdf. ots) attached. Companion repository: Lean 4 + Mathematica kernel certificates at github. com/ChristianFranchi/Brahman/tree/main/Electrons/DarkEnergy. Author: Christian Franchi Viceré, A. I. Visions LTD (London, UK), ORCID 0009-0001-8974-4991.